Simplify to lowest terms. $\dfrac{30}{45}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 30 and 45? $30 = 2\cdot3\cdot5$ $45 = 3\cdot3\cdot5$ $\mbox{GCD}(30, 45) = 3\cdot5 = 15$ $\dfrac{30}{45} = \dfrac{2 \cdot 15}{ 3\cdot 15}$ $\hphantom{\dfrac{30}{45}} = \dfrac{2}{3} \cdot \dfrac{15}{15}$ $\hphantom{\dfrac{30}{45}} = \dfrac{2}{3} \cdot 1$ $\hphantom{\dfrac{30}{45}} = \dfrac{2}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{30}{45}= \dfrac{3\cdot10}{3\cdot15}= \dfrac{3\cdot 5\cdot2}{3\cdot 5\cdot3}= \dfrac{2}{3}$